Electronic gaming machines (EGMs) operable to enable play of wagering games are well known. A typical wagering game includes a primary game, and certain wagering games also include a bonus game. Generally, these EGMs initiate a play of the primary game following: (1) receipt of a wager input (such as an actuation of a wager button) that indicates how much the player desires to wager; and/or (2) receipt of a game initiation input (such as an actuation of a play button). Many of these EGMs determine any primary awards for a wagered-on play of the primary game based on the outcome of the play of the primary game and the wager amount. Typically, the larger the wager amount, the larger the primary award (for the same outcome). Winning outcomes that are less likely to occur usually result in larger primary awards than winning outcomes that are more likely to occur. EGMs operable to enable play of a bonus game usually initiate a play of the bonus game upon an occurrence of a bonus triggering event. These EGMs determine any bonus awards for the play of the bonus game based on the outcome of the play of the bonus game and the wager amount.